## Relativistic Celestial Mechanics of the Solar System (Google eBook)This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping. |

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### Contents

1 | |

Section 2 | 81 |

Section 3 | 85 |

Section 4 | 117 |

Section 5 | 163 |

Section 6 | 186 |

Section 7 | 199 |

Section 8 | 248 |

Section 18 | 519 |

Section 19 | 605 |

Section 20 | 609 |

Section 21 | 614 |

Section 22 | 645 |

Section 23 | 669 |

Section 24 | 671 |

Section 25 | 672 |

Section 9 | 257 |

Section 10 | 330 |

Section 11 | 371 |

Section 12 | 385 |

Section 13 | 415 |

Section 14 | 423 |

Section 15 | 429 |

Section 16 | 449 |

Section 17 | 463 |

Section 26 | 701 |

Section 27 | 715 |

Section 28 | 766 |

Section 29 | 804 |

Section 30 | 813 |

Section 31 | 819 |

Section 32 | 825 |

### Common terms and phrases

acceleration affine connection angle approximation Astrometry Astronomical Astrophysics barycentric binary body body’s Brumberg calculation Celestial Mechanics Celestial Reference center of mass Chap Christoffel symbols components constant coordinate system covector Damour defined deflection dynamical Earth Einstein energy-momentum tensor ephemeris equations of motion equinox field equations four-velocity function gauge GCRS geocentric geodesic global coordinates gravitational field gravitational potential gravitational waves IAU Resolutions ICRS inertial frame integral Klioner Kopeikin le-tex light light-ray linear Lorentz manifold mathematical matrix measured metric tensor Minkowski spacetime multipole moments N-body system Newtonian nutation observer ofthe Solar System orbital parameter partial derivatives particle perturbation Physical Review planet post-Newtonian precession propagation pulsar reference frame Reference System relativistic Relativistic Astrometry Relativistic Celestial Mechanics respect rotation scalar field Section Soffel solution space spatial special relativity speed theory of gravity tion two-body problem unit vector vector field velocity worldline